Network management based on modeling of cascading effect of failure

ABSTRACT

A system and method of managing a network with assets are described. The method includes generating a directed graph with each of the assets represented as a node, determining individual failure probability of each node, computing downstream failure probability of each node according to an arrangement of the nodes in the directed graph, computing upstream failure probability of each node according to the arrangement of the nodes in directed graph, and computing network failure probability for each node based on the corresponding individual failure probability, the downstream failure probability, and the upstream failure probability. Managing the network is based on the network failure probability of the assets.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/665,316, filed on Mar. 23, 2015 and entitled “NETWORK MANAGEMENTBASED ON MODELING OF CASCADING EFFECT OF FAILURE”, which is incorporatedherein by reference in its entirety.

BACKGROUND

The present invention relates to management of a network, and morespecifically, to network management based on modeling of the cascadingeffect of failures.

There are many types of networks that include a number of assets thataffect each other. Exemplary networks with a number of interdependentassets include a power network (power grid), gas network, and a waternetwork. For example, a power network includes electrical assets (e.g.,transformers, switches, fuses) and non-electrical assets (e.g., supportstructures, poles), each of which can not only fail but also damageother assets within the network.

SUMMARY

According to one embodiment of the present invention, a method ofmanaging a network with assets includes generating, using a processor, adirected graph with each of the assets represented as a node;determining individual failure probability of each node; computing,using the processor, downstream failure probability of each nodeaccording to an arrangement of the nodes in the directed graph;computing, using the processor, upstream failure probability of eachnode according to the arrangement of the nodes in the directed graph;computing network failure probability for each node based on thecorresponding individual failure probability, the downstream failureprobability, and the upstream failure probability; and managing thenetwork based on the network failure probability of the assets.

According to another embodiment, a network management system to manageassets of the network includes a memory device configured to storeinstructions, and a processor configured to process the instructions tocompute network failure probability associated with each asset based ondetermining individual failure probability, upstream failureprobability, and downstream failure probability for each asset, and tomanage the network based on the network failure probabilities of theassets.

According to yet another embodiment, a computer program product includesa tangible storage medium readable by a processing circuit and storinginstructions for execution by the processing circuit to perform a methodof managing a network with assets. The method includes generating adirected graph with each of the assets represented as a node;determining individual failure probability of each node; computingdownstream failure probability of each node according to an arrangementof the nodes in the directed graph; computing upstream failureprobability of each node according to the arrangement of the nodes inthe directed graph; computing network failure probability for each nodebased on the corresponding individual failure probability, thedownstream failure probability, and the upstream failure probability;and managing the network based on the network failure probability of theassets.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail herein and are considered a part of the claimedinvention. For a better understanding of the invention with theadvantages and the features, refer to the description and to thedrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 is a process flow of a method of managing a network according toembodiments of the invention;

FIG. 2 is an exemplary graph used to identify nodes and connections forembodiments of the invention;

FIG. 3 shows processes involved in computing downstream failureprobability at block 130 (FIG. 1 ) for every node according to anembodiment;

FIG. 4 shows the processes involved in computing upstream failureprobability for a given node at block 140 (FIG. 1 ) according to anembodiment;

FIG. 5 shows the processes involved in computing physical failureprobability for each node at block 150 (FIG. 1 ) according to anembodiment;

FIG. 6 shows the processes involved in computing network failureprobability for each node at block 160 (FIG. 1 ) according to anembodiment; and

FIG. 7 is a block diagram of a processing system to implementembodiments of the invention.

DETAILED DESCRIPTION

As noted above, a network may include a number of assets whose failureaffects the individual asset as well as other assets of the network. Anaccurate assessment of failures and the cascading effect of failures inthe network facilitate management of the network. The areas ofvulnerability may be identified and addressed. Embodiments of themethods and systems discussed herein relate to modeling the cascadingeffect of failures in a network and managing the network accordingly.While a power network and associated (electrical and non-electrical)assets are discussed below for explanatory purposes, the embodimentsdetailed herein are not limited to any one particular type of network.

FIG. 1 is a process flow of a method of managing a network according toembodiments of the invention. Throughout the discussion herein, assetand node are used interchangeably because the representation of theassets in a directed graph is as nodes. At block 110, generating adirected graph including different node types refers to known techniquesfor graphing the nodes of the network in a way that shows theirinterconnections, as further discussed and illustrated below.Determining individual failure probability of every node in the graph atblock 120 is independent of interrelationships among nodes, as discussedbelow. Computing downstream failure probability for every node in thegraph, at block 130, involves computing the probability of a failuredownstream of a given node due to the given node, as detailed below.Computing the upstream failure probability for a given node, at block140, involves an iterative process starting at the first or root node ofthe graph, as detailed below. The processes include computing physicalfailure probability for the given node at block 150 and computingnetwork failure probability for the given node at block 160. Based onthe computations and determinations that are further discussed below,managing the network at block 170 may include mitigating failures basedon their probability.

FIG. 2 is an exemplary graph 200 used to identify nodes 210 andconnections 220 for embodiments of the invention. Several nodes 210 ofelectrical and non-electrical (physical) assets are shown withconnections 220 indicating the physical topology of the network. In theexemplary graph 200, the nodes 210 include non-electrical or physicalassets—poles p1, p2—and electrical assets—transformers t1, t2, cablesc1, c2, source pp, and endpoint s2—as well as an electrical protectivedevice (e.g., fuse) dpd1. Steps involved in the generation of the graph200 are known and are not detailed here. Generally, the physicaltopology is converted into a list of edges. Each edge is an ordered pairof two assets, and it is assumed that electric power flows from thefirst asset to the second in the ordered pair. The assets arerepresented by the nodes 210 and the connectivity 220 is defined by theedges. Each of the nodes 210 is classified as a protective electricalasset (e.g., fuse, dynamic protective device) that is able to stop thepropagation of a failure, a non-protective electrical asset (e.g.,transformer) that does not have any inbuilt protective feature, or aphysical asset (e.g., pole) that only has the purpose to house orsupport an electrical asset in some way. In the exemplary graph 200, thenode 210 pp is the root node (first electrical asset) for purposes ofdetermining upstream failure probability (140, FIG. 1 ), which isdetailed further below. As noted above, the embodiments detailed hereinare not limited to a power network. In a gas network, for example, theassets may be protective gas assets (e.g., check valves), gas assets(e.g., gas pipes, junctions, pumps), and physical assets (e.g., the pipesection supports).

The individual failure probability of each node is determined at block120 as:P _(f)(i)∀i∈N  [EQ. 1]

N is the set of all nodes of the graph (e.g., all nodes 210 of graph200, FIG. 2 ). The reliability R(i) of a given node i may be computedfrom the failure probability as:R(i)=1−P _(f)(i)  [EQ. 2]

The processes involved in determining individual failure includeinvestigating historical failures of each recorded asset failureincident over a specified time period and determining the relationshipof the failure rate with attributes of the asset such as, for example,asset type, make, material, and age in order to generate a trainingmodel. Once the training model has been generated, failure rates for allnodes (i.e., assets with and without recorded failure histories) may beextrapolated from the training model.

FIG. 3 shows processes involved in computing downstream failureprobability at block 130 (FIG. 1 ) for every node according to anembodiment. At block 310, performing a breadth first search (BFS)involves traversing the graph (e.g., 200 in FIG. 2 ) by beginning withthe root node (e.g., pp in FIG. 2 ) and progressing through the nodes(210, FIG. 2 ) one-at-a-time from the root to its neighbors. At block320, identifying and populating two sets of (downstream) children nodesP and Q using depth first search (DFS) means that each branch from theroot node to the last node of the branch is traversed beforeback-tracking to explore each node of the next branch all the waythrough. P refers to all non-protective electrical assets that aredownstream of the current node and which do not have a protectiveelectrical asset in the path to the current node. If P is beingcalculated for a sub-node in a branch (in the recursive part of the DFSalgorithm), then the P of the current node should not include elementsfrom the P set of the main node of the branch (i.e., elements of the Pset will not be repeated). Q refers to all protective electrical assetsthat are downstream of the current node and do not have any otherprotective electrical assets in the path to the current node. As anexample, if c1 shown in FIG. 2 were the current node, the P would be anempty set due to the protective electrical asset dpd1 (every otherdownstream node would have dpd1 in the path to c1, the current node),which is the next node after c1, and Q would include dpd1.

Based on the definitions of P and Q, the current node may be thought ofas being in series with every element in P. That is, because of theabsence of a protective electrical asset between the current node andthe elements of P, a failure at any node that is an element in P cantrigger a failure in the current node. Further, the current node may bethought of as being in series with every element in Q. However, thefailure propagation is less straight-forward in this case. Two sub-casesemerge in considering the failure in an element (node) of Q. In a firstcase, when the protective electrical asset that is an element of Q worksas expected, then any downstream failure in a node downstream of theprotective electrical device (element of Q) will not affect the currentnode. In the second case, however, when the protective electrical asset(element of Q) fails, then a failure in a node downstream of theprotective electrical asset (and the current node) will propagate andcause the current node to fail, as well. Both of these cases must beconsidered.

At block 330, it is determined if Q (the set of protective electricalassets downstream of the current node) is empty. If Q is not empty,then, at block 340, each element of Q is made the current node, and, atblock 320, P and Q are identified for each current node. If Q is empty,then, at block 350, computing downstream failure probability for thecurrent node i is performed. The probability of downstream failure(P_(df)) for the i^(th) node is given by:P _(df)(i)=1−R _(df)(i)  [EQ. 3]

R_(df) is the downstream reliability of the current node and, with Rindicating reliability, is given by:

$\begin{matrix}{{R_{df}(i)} = {\prod\limits_{j \in P}\;{{R(j)}{\prod\limits_{k \in Q}\;\left\lbrack {{R(k)} + {\left( {1 - {R(k)}} \right){R_{df}(k)}}} \right\rbrack}}}} & \left\lbrack {{EQ}.\mspace{14mu} 4} \right\rbrack\end{matrix}$

At block 360, following computation of the probability of downstreamfailure, setting the next node in the graph as the current node is perthe BFS.

FIG. 4 shows the processes involved in computing upstream failureprobability for a given node at block 140 (FIG. 1 ) according to anembodiment. At block 410, performing breadth-first searching (BFS) ofthe graph (e.g., 200, FIG. 2 ) involves beginning at the root node andmoving through the graph to consider each node the current nodeone-at-a-time, as noted above. At block 420, it is determined whetherthe current node is the root node. If the current node is the root node,then the upstream failure probability of the current node is set to 0 atblock 430. This is because the root node is the most upstream node inthe graph (see e.g., p1 in FIG. 2 ). Thus, the probability of a failureupstream of the root node is 0. From block 430, the process at block 150(FIG. 1 ) is performed at block 500, as detailed below. If the currentnode is not the root node, then, at block 440, determining Si, the setof inbound nodes of the current node i is performed. The set of inboundnodes is the set of immediate parents of the current node i. At block450, it is determined whether the network failure probability hasalready been computed for every node that is an element of the set Si.As detailed below with reference to EQ. 5, the network failureprobability of every node in the set Si is determined using a modifieddirected graph G′ that excludes the current node i. The network failureprobability refers to the process completed at block 160 (FIG. 1 ) forthe parent nodes (using G′). That is, because a current node may havemultiple nodes in the set Si (multiple immediate parents), the loopdefined by blocks 450, 460, and 470 ensures that the process shown atFIGS. 4 through 6 is completed for every parent node before the childnode is evaluated.

If it is determined at block 450 that the network failure probabilityhas not been computed for every node in the set Si of the current node,then, at block 460, the nodes in Si that have not had network failureprobability computed are added to an evaluation list. At block 470, thenodes in the evaluation list are added as nodes to visit (i.e., nodes toprocess according to the steps shown in FIG. 4 ). If it is determined atblock 450 that the network failure probability (P_(inf)) has beencomputed for every node in the set Si of the current node (everyimmediate parent of the current node), then, at block 480, upstreamfailure probability is computed for the current node i. The computationof upstream failure probability P_(uf) of node i is given by:

$\begin{matrix}{{P_{uf}(i)} = {\prod\limits_{j \in S_{i}}\;{P_{{ufG}^{\prime}}(j)}}} & \left\lbrack {{EQ}.\mspace{14mu} 5} \right\rbrack\end{matrix}$

The computation at EQ. 5 requires consideration of a modified directedgraph G′ in which the current node i is omitted. The upstream failureprobability of the current node i is based on the network failureprobability of each immediate parent node of node i (each node in theset Si). By determining the network failure probability of each node inthe set Si based on the modified directed graph G′ (which does notinclude the current node i), the failure probabilities of nodesdownstream of i (in the original directed graph) are not countedmultiple times (once for each j). Once the upstream failure probabilityis computed at block 480, the node i is removed from the evaluation listat block 490 and the next node is considered at block 410. Additionally,once the upstream failure probability is computed at block 480, theprocess at block 150 (FIG. 1 ) is performed at block 500 as detailedbelow.

FIG. 5 shows the processes 500 involved in computing physical failureprobability for each node at block 150 (FIG. 1 ) according to anembodiment. As FIG. 4 indicates and as discussed above, the processes500 to implement block 150 (FIG. 1 ) are reached in multiple ways, eachof which ensures that the physical failure probability is considered foreach node as the current node. At block 510, determining the set ofnodes Bi includes determining the set of physical assets connected tothe current node i. In the exemplary graph 200 of FIG. 1 , if thecurrent node were pp, then the set of Bi would be comprised of p1, thepole that is directly connected to pp. The pole p2 is not part of Biwhen the current node is pp. At block 520, iterating through eachelement j of Bi begins, at block 530, with determining if the currentnode i is the first node among the nodes (electrical assets) that areconnected to element j of the set Bi. That is, in the example discussedwith reference to FIG. 2 , if pp were the current node i, then pp is thefirst node (according to the directed graph) among the electrical assetsthat are connected to p1 when j is such that the element of Bi is p1. Ifthe current node i is not the first node among the (electrical asset)nodes that are connected to the current j element of Bi, then processingreturns to block 520 to select the next element in Bi. If the currentnode i is the first node among the (electrical asset) nodes that areconnected to the current j element of Bi, then the physical asset j isadded to Ai, which is the set of physical assets that have node i as thefirst (electrical) asset in the group of assets the physical assetsupports, at block 540. From block 540, the next physical asset j isselected at block 520.

When all the physical assets in Bi have been processed, then, at block550, it is determined if Ai is an empty set. That is, it is determinedif there are no physical assets for which the current node i is thefirst electrical asset in the group of assets that the physical assetsupports. In exemplary FIG. 2 , t1, for example, is not the first nodesupported by any physical asset. Thus, if the current node were t1, theresulting Ai would be an empty set. When Ai is an empty set, then thephysical failure probability is set to 0 at block 560. When Ai is not anempty set, then the physical failure probability is computed at block570. The computation of the physical failure probability is given by:

$\begin{matrix}{{P_{pf}(i)} = {\prod\limits_{j \in A_{i}}\;{P_{f}(j)}}} & \left\lbrack {{EQ}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

Whether the physical failure probability is computed (at block 570) orset to 0 (at block 560), the process at block 160 (FIG. 1 ) is thenperformed as discussed with reference to FIG. 6 .

FIG. 6 shows the processes 600 involved in computing network failureprobability for each node at block 160 (FIG. 1 ) according to anembodiment. At block 610, network reliability for the current node i iscomputed as a product of downstream reliability, upstream reliability,individual reliability, and physical reliability. This networkreliability is given by:R _(nf)(i)=R(i)·R _(df)(i)·R _(uf)(i)·R _(pf)(i)  [EQ. 7]EQ. 7 can also be written as:R _(nf)(i)=(1−P _(f)(i))·(1−P _(df)(i))·(1−P _(uf)(i))·(1−P_(pf)(i))  [EQ. 8]

Based on the computed network reliability, network failure probabilityassociated with the current node i may be computed as:P _(nf)(i)=1−R _(nf)(i)  [EQ. 9]

The processes detailed above provide information about the probabilityof network failure associated with each given electrical asset. As such,at block 70 (FIG. 1 ), management of the network can take into accountthe information generated by the other processes. For example, a node(electrical asset) with a high P_(nf) according to EQ. 9 may bescheduled for inspection and maintenance more frequently than a nodewith a relatively lower P_(nf). As another example, a threshold may beset for the P_(nf) of any node such that any node whose P_(nf) exceedsthe threshold will be maintained as a critical asset. That maintenancemay entail more frequency inspection and testing or replacement, forexample.

FIG. 7 is a processing system 700 configured to implement embodimentsdescribed herein. The processes detailed herein may be implemented byone or more processors (processing circuits) 710 based on instructionsstored in one or more memory devices 720. The memory devices 720 mayadditionally store the training model discussed with reference to block120 (FIG. 1 ), for example. The instructions and one or more memorydevices 720 represent a computer program product to implement thedetailed processes. The processing system 700 may additionally includean input interface 730 (e.g., keyboard, wired or wireless communicationlink) to receive commands or data, as well as an output interface 740(e.g., display device, communication link) to send output. The computerprogram product (720) and processor 710 may be stand-alone components ormay be integrated with other components of the network.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

The flow diagrams depicted herein are just one example. There may bemany variations to this diagram or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps may be performed in a differing order or steps maybe added, deleted or modified. All of these variations are considered apart of the claimed invention. Further, as noted above, although anelectrical network is predominantly discussed as an exemplary network,the flow diagrams herein and the discussion pertain to any network withassets in which failures may propagate in both directions from theperspective of a directed graph.

While the preferred embodiment to the invention had been described, itwill be understood that those skilled in the art, both now and in thefuture, may make various improvements and enhancements which fall withinthe scope of the claims which follow. These claims should be construedto maintain the proper protection for the invention first described.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A method of managing a network with utilityassets of an electrical grid, the method comprising: generating, using aprocessor, a directed graph with each of the utility assets representedas a node in the directed graph, the utility assets including electricalassets of the electrical grid; determining a historical failure rate foreach node of at least a portion of the utility assets over apredetermined period of time; determining a relationship of thehistorical failure rates with one or more physical attributes of one ormore of the utility assets; generating a training model based on thehistorical failure rates and the relationships of the historical failurerates with the one or more physical attributes of the one or moreutility assets; determining, using the training model, an individualfailure probability of each node; computing, using the processor, adownstream failure probability of each of at least a subset of the nodesof the directed graph according to an arrangement of the nodes in thedirected graph, the computing the downstream failure probabilityincluding: determining whether a path between a selected node of the atleast a subset of nodes and a particular node of the directed graph, andcomputing the downstream failure probability of the selected node basedon the determination regarding the path; computing, using the processor,an upstream failure probability of each node of the at least the subsetof nodes according to the arrangement of the nodes in the directedgraph; computing a network failure probability for each node of the atleast the subset of nodes based on the corresponding individual failureprobability, the corresponding downstream failure probability, and thecorresponding upstream failure probability; and increasing frequency ofinspection of one or more nodes based on the network failure probabilityof the nodes probability.
 2. The method according to claim 1, furthercomprising classifying each node in the directed graph.
 3. The methodaccording to claim 2, wherein the network is an electric power networkand the classifying each node includes classifying each node as anon-protective electrical asset, a protective electrical asset, or aphysical asset.
 4. The method according to claim 3, wherein theprotective electrical asset stops the propagation of a failure of one ormore other assets through the electrical grid.
 5. The method accordingto claim 1, wherein the determining the individual failure probabilityof each node includes extrapolating from the training model that istrained with historical data.
 6. The method according to claim 1,wherein the computing the downstream failure probability for each nodeis based on a classification of one or more assets downstream of thenode.
 7. The method according to claim 1, wherein the computing theupstream failure probability for each node involves an iterativeprocess.
 8. The method according to claim 7, wherein the computing theupstream failure probability for each node is based on the networkfailure probability of upstream nodes of a modified directed graph thatomits the node.
 9. The method according to claim 7, wherein thecomputing the network failure probability for each node is also based ona physical failure probability.
 10. The method according to claim 1,wherein the managing the network based on the network failureprobability of the utility assets includes setting a threshold networkfailure probability and, when the network failure probability of one ofthe utility assets exceeds the threshold network failure probability,managing the one of the utility assets as a critical asset.
 11. Themethod according to claim 1, wherein, the physical attributes includesan asset type, an asset make, an asset material, or an asset age.
 12. Anontransitory computer readable medium including executableinstructions, the instructions being executable by one or moreprocessors to perform a method for managing a network with utilityassets of an electrical grid, the method comprising: generating adirected graph with each of the utility assets represented as a node inthe directed graph, the utility assets including electrical assets ofthe electrical grid; determining a historical failure rate for each nodeof at least a portion of the utility assets over a predetermined periodof time; determining a relationship of the historical failure rates withone or more physical attributes of one or more of the utility assets;generating a training model based on the historical failure rates andthe relationships of the historical failure rates with the one or morephysical attributes of the one or more utility assets; determining,using the training model, an individual failure probability of eachnode; computing a downstream failure probability of each of at least asubset of the nodes of the directed graph according to an arrangement ofthe nodes in the directed graph, the computing the downstream failureprobability including: determining whether a path between a selectednode of the at least a subset of nodes and a particular node of thedirected graph, and computing the downstream failure probability of theselected node based on the determination regarding the path; computingan upstream failure probability of each node of the at least the subsetof nodes according to the arrangement of the nodes in the directedgraph; computing a network failure probability for each node of the atleast the subset of nodes based on the corresponding individual failureprobability, the corresponding downstream failure probability, and thecorresponding upstream failure probability; and increasing frequency ofinspection of one or more nodes based on the network failure probabilityof the nodes probability.
 13. The nontransitory computer readable mediumaccording to claim 12, the method further comprising classifying eachnode in the directed graph.
 14. The nontransitory computer readablemedium according to claim 13, wherein the network is an electric powernetwork and the classifying each node includes classifying each node asa non-protective electrical asset, a protective electrical asset, or aphysical asset.
 15. The nontransitory computer readable medium accordingto claim 14, wherein the protective electrical asset stops thepropagation of a failure of one or more other assets through theelectrical grid.
 16. The nontransitory computer readable mediumaccording to claim 12, wherein the determining the individual failureprobability of each node includes extrapolating from the training modelthat is trained with historical data.
 17. The nontransitory computerreadable medium according to claim 12, wherein the computing thedownstream failure probability for each node is based on aclassification of one or more assets downstream of the node.
 18. Thenontransitory computer readable medium according to claim 12, whereinthe computing the upstream failure probability for each node involves aniterative process.
 19. The nontransitory computer readable mediumaccording to claim 18, wherein the computing the upstream failureprobability for each node is based on the network failure probability ofupstream nodes of a modified directed graph that omits the node.
 20. Thenontransitory computer readable medium according to claim 18, whereinthe computing the network failure probability for each node is alsobased on a physical failure probability.
 21. The nontransitory computerreadable medium according to claim 12, wherein the managing the networkbased on the network failure probability of the utility assets includessetting a threshold network failure probability and, when the networkfailure probability of one of the utility assets exceeds the thresholdnetwork failure probability, managing the one of the utility assets as acritical asset.
 22. The nontransitory computer readable medium accordingto claim 12, wherein, the physical attributes includes an asset type, anasset make, an asset material, or an asset age.
 23. A system comprising:one or more processors; and memory including instructions executable bythe one or more processors to: generate a directed graph with each ofutility assets represented as a node in the directed graph, the utilityassets including electrical assets of an electrical grid; determine ahistorical failure rate for each node of at least a portion of theutility assets over a predetermined period of time; determine arelationship of the historical failure rates with one or more physicalattributes of one or more of the utility assets; generate a trainingmodel based on the historical failure rates and the relationships of thehistorical failure rates with the one or more physical attributes of theone or more utility assets; determine, using the training model, anindividual failure probability of each node; compute a downstreamfailure probability of each of at least a subset of the nodes of thedirected graph according to an arrangement of the nodes in the directedgraph, the computing the downstream failure probability including theone or more processors to: determine whether a path between a selectednode of the at least a subset of nodes and a particular node of thedirected graph, and compute the downstream failure probability of theselected node based on the determination regarding the path; compute anupstream failure probability of each node of the at least the subset ofnodes according to the arrangement of the nodes in the directed graph;compute a network failure probability for each node of the at least thesubset of nodes based on the corresponding individual failureprobability, the corresponding downstream failure probability, and thecorresponding upstream failure probability; and increase frequency ofinspection of one or more nodes based on the network failure probabilityof the nodes probability.